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authorsijanec <anton@sijanec.eu>2021-04-17 21:14:22 +0200
committersijanec <anton@sijanec.eu>2021-04-17 21:14:22 +0200
commit632a2df639479b919c13648bd8f13a186478810d (patch)
tree6d76d586a002a84b942d7a9c22f011e4485531bf /mat/domace_naloge/31
parentla artikolo ~ (diff)
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Diffstat (limited to 'mat/domace_naloge/31')
-rw-r--r--mat/domace_naloge/31/dokument.aux35
-rw-r--r--mat/domace_naloge/31/dokument.log1852
-rw-r--r--mat/domace_naloge/31/dokument.out1
-rw-r--r--mat/domace_naloge/31/dokument.pdfbin0 -> 73728 bytes
-rw-r--r--mat/domace_naloge/31/dokument.synctex.gzbin0 -> 27563 bytes
-rw-r--r--mat/domace_naloge/31/dokument.tex238
-rw-r--r--mat/domace_naloge/31/stderr.log1
-rw-r--r--mat/domace_naloge/31/stdout.log808
8 files changed, 2935 insertions, 0 deletions
diff --git a/mat/domace_naloge/31/dokument.aux b/mat/domace_naloge/31/dokument.aux
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+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codered}{rgb}{1,0,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\renewcommand{\dateseparator}{. }
+\settimeformat{hhmmsstime}
+\lstdefinestyle{mystyle}{
+ backgroundcolor=\color{backcolour},
+ commentstyle=\color{codegreen},
+ keywordstyle=\color{magenta},
+ numberstyle=\tiny\color{codegray},
+ stringstyle=\color{codepurple},
+ basicstyle=\ttfamily\footnotesize,
+ breakatwhitespace=false,
+ breaklines=true,
+ captionpos=b,
+ keepspaces=true,
+ numbers=left,
+ numbersep=5pt,
+ showspaces=false,
+ showstringspaces=false,
+ showtabs=false,
+ tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
+ \newpage
+ \null
+ \vskip 2em%
+ \begin{center}%
+ \let \footnote \thanks
+ {\LARGE \@title \par}%
+ \vskip 1.5em%
+ {\large
+ \lineskip .5em%
+ \begin{tabular}[t]{c}% <------
+ \@author% <------ Authors
+ \end{tabular}\par}% <------
+ \vskip 1em%
+ {\large \@date}%
+ \end{center}%
+ \par
+ \vskip 1.5em}
+%opening
+\newcommand{\snovdn}{Transformacije na ravnini }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{31}
+\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
+\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
+\makeatletter
+\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
+\newcommand{\@xslalph}[1]{%
+ \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
+ \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
+ \or t\or u\or v\or z\or \v{z}
+ \else\@ctrerr\fi%
+}
+\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+ \frac{\text{#1}}{\text{#2}}
+}
+\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
+\newcommand\vektor{\overrightarrow}
+\newcommand{\iic}{I\textsuperscript{2}C }
+\title{%
+ \snovdn --- \stevilkadn. domača naloga
+ \\
+ \large Matematika, Gimnazija Bežigrad}
+\author{\begin{tabular}{rl}
+ \textbf{Profesor:} & prof. Vilko Domajnko \\
+ \textbf{Avtor:} & Anton Luka Šijanec, 2. a
+% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
+\end{tabular}}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}%
+\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
+\everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+\begin{abstract}
+Ta dokument vsebuje navodila in rešitve domače naloge snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam.
+\end{abstract}
+\paragraph{Navodilo naloge} \textbf{Mat3} (Mat2 verjetno): 114 / 1, 2, 3
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \item Prezrcali graf funkcije $f\left(x\right)=-\frac{1}{2}x+2$
+ \begin{tasks}[label=\textbf{\xslalph*)}](2)
+ \task čez abscisno os,
+ \task čez ordinatno os,
+ \task čez koordinatno izhodišče,
+ \task čez simetralo lihih kvadrantov
+ \end{tasks}
+ \begin{tikzpicture}
+ \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
+ \addplot[black, solid] (x, {(-1/2)*x+2}) node[above,pos=.6] {$f$};
+ \addplot[black, densely dotted] (x, {-1*((-1/2)*x+2)}) node[above,pos=.6] {$a$};
+ \addplot[black, densely dashed] (x, {(1/2)*x+2}) node[above,pos=.6] {$b$};
+ \addplot[red, solid] (x, {(-1/2)*x-2}) node[above,pos=.6] {$c$};
+ \addplot[red, densely dotted] (x, {(-2)*x+4}) node[above,pos=.6] {$č$};
+ \addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x+2$}}
+ \addlegendentry{$a(x) = f\left(x\right)\cdot-1$}
+ \addlegendentry{\raisebox{7pt}{$b(x) = \frac{1}{2}x+2$}}
+ \addlegendentry{\raisebox{7pt}{$c(x) = -\frac{1}{2}x-2$}}
+ \addlegendentry{\raisebox{7pt}{$č(x) = -2x+4$}}
+ \end{axis}
+ \end{tikzpicture}
+ \newpage
+ \item Nariši grafa funkcij.
+ \begin{tasks}[label=\textbf{\xslalph*)}](2)
+ \task $f\left(x\right)=-\frac{1}{2}x+1$ in $g\left(x\right)=-2f\left(x\right)$
+ \task \color{red} $f\left(x\right)=-2x+1$ in $g\left(x\right)=f\left(3x\right)$ \color{black}
+ \task \color{green} $f\left(x\right)=\frac{1}{2}x-1$ in $g\left(x\right)=f\left(\frac{1}{2}x\right)$ \color{black}
+ \task \color{blue} $f\left(x\right)=-\frac{1}{2}x-3$ in $g\left(x\right)=\frac{1}{2}f\left(x\right)$ \color{black}
+ \end{tasks}
+ \begin{tikzpicture}
+ \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
+ \addplot[black, solid] (x, {(-1/2)*x+1});
+ \addplot[black, densely dashed] (x, {-2*((-1/2)*x+1)});
+ \addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x+1$}}
+ \addlegendentry{$g(x) = -2f\left(x\right)$}
+ \addplot[red, solid] (x, {-2*x+1});
+ \addplot[red, densely dashed] (x, {-2*3*x+1});
+ \addlegendentry{$f(x) = -2x+1$}
+ \addlegendentry{$g(x) = f(3x)$}
+ \addplot[green, solid] (x, {(1/2)*x-1});
+ \addplot[green, densely dashed] (x, {(1/2)*(1/2)*x-1});
+ \addlegendentry{\raisebox{7pt}{$f(x) = \frac{1}{2}x-1$}}
+ \addlegendentry{\raisebox{7pt}{$g(x) = f\left(\frac{1}{2}x\right)$}}
+ \addplot[blue, solid] (x, {(-1/2)*x-3});
+ \addplot[blue, densely dashed] (x, {(1/2)*((-1/2)*x-3)});
+ \addlegendentry{\raisebox{7pt}{$f(x) = -\frac{1}{2}x-3$}}
+ \addlegendentry{\raisebox{7pt}{$g(x) = \frac{1}{2}f(x)$}}
+ \end{axis}
+ \end{tikzpicture}
+ \newpage
+ \item Nariši grafa funkcij.
+ \begin{tasks}[label=\textbf{\xslalph*)}](2)
+ \task $f\left(x\right)=-3x+1$ in $g\left(x\right)=f\left(x-3\right)$
+ \task \color{red} $f\left(x\right)=4x+3$ in $g\left(x\right)=f\left(x+1\right)$ \color{black}
+ \task \color{green} $f\left(x\right)=3x-1$ in $g\left(x\right)=f\left(x-1\right)-3$ \color{black}
+ \task \color{blue} $f\left(x\right)=-4x-1$ in $g\left(x\right)=f\left(x+2\right)-3$ \color{black}
+ \end{tasks}
+ \begin{tikzpicture}
+ \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}]
+ \addplot[black, solid] (x, {-3*x+1});
+ \addplot[black, densely dashed] (x, {-3*(x-3)+1});
+ \addlegendentry{$f(x) = -3x+1$}
+ \addlegendentry{$g(x) = f(x-3)$}
+ \addplot[red, solid] (x, {4*x+3});
+ \addplot[red, densely dashed] (x, {4*(x+1)+3});
+ \addlegendentry{$f(x) = 4x+3$}
+ \addlegendentry{$g(x) = f(x+1)$}
+ \addplot[green, solid] (x, {3*x-1});
+ \addplot[green, densely dashed] (x, {(3*(x-1)-1)-3});
+ \addlegendentry{$f(x) = 3x-1$}
+ \addlegendentry{$g(x) = f(x-1)-3$}
+ \addplot[blue, solid] (x, {-4*x-1});
+ \addplot[blue, densely dashed] (x, {(-4*(x+2)-1)-3});
+ \addlegendentry{$f(x) = -4x-1$}
+ \addlegendentry{$g(x) = f(x+2)-3$}
+ \end{axis}
+ \end{tikzpicture}
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2021} ali \texttt{TeXLive 2020}.}
+izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
+\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi
+\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
+\if\razhroscevanje1
+\vfill
+\section*{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
+
+Grafi imajo natančnost \functionSamples\space točk na graf.
+
+Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+% \item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}
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